Divide 500 into two parts such that the ratio of one to the other are in 5 : 3?

Options

A. 312.5, 187.5
B. 308.5, 191.5
C. 280, 220
D. 300, 200

Answer

To solve the problem of dividing 500 into two parts in the ratio of 5:3, we can follow these steps:

### Step 1: Define the Parts
Let the two parts be represented as \(5x\) and \(3x\), where \(x\) is a common multiplier.

### Step 2: Set Up the Equation
According to the problem, the sum of the two parts should equal 500. Therefore, we can write the equation:
\[ 5x + 3x = 500 \]

### Step 3: Simplify the Equation
Combine like terms:
\[ 8x = 500 \]

### Step 4: Solve for \(x\)
To find \(x\), divide both sides of the equation by 8:
\[ x = \frac{500}{8} = 62.5 \]

### Step 5: Calculate the Two Parts
Now that we have the value of \(x\), we can find the two parts:
- The first part, \(5x\):
\[ 5x = 5 \times 62.5 = 312.5 \]
- The second part, \(3x\):
\[ 3x = 3 \times 62.5 = 187.5 \]

### Final Answer
Thus, the two parts are:
- First part: \(312.5\)
- Second part: \(187.5\)